The first two authors have recently defined Rabinowitz Floer homology groups RFH_*(M,W) associated to a separating exact embedding of a contact manifold (M, e) into a symplectic manifold (W,ω). These depend only on the bounded component V of W M. We construct a long exact sequence in which symplectic cohomology of V maps to symplectic homology of V, which in turn maps to Rabinowitz Floer homology RFH_*(M,W), which then maps to symplectic cohomology of V. We compute RFH_*(ST~* L,T~* L), where ST~* L is the unit cosphere bundle of a closed manifold L. As an application, we prove that the image of a separating exact contact embedding of ST~* L cannot be displaced away from itself by a Hamiltonian isotopy, provided dim L ≥ 4 and the embedding induces an injection on π1.
展开▼
